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## Triangle – Area problem

In triangle ABC, cevians AD, BE and CF intersect at point P. The areas of triangles PAF, PFB, PBD and PCE are 40, 30, 35 and 84, respectively. Find the area of triangle ABC.

TIPS:Let the area of triangle PEA be x and area of triangle PCD be y . Now use the proportion of areas of triangles.

$\frac{y}{35} = \frac{ 84+ x +y }{105} \: and \: \frac{84}{x} = \frac{ 119+y }{ 70 + x }$

Now use system of linear equations and find x and y . The area of triangle ABC is 189+x+y .